No 44

Unionization Structures in International Oligopoly

Beatrice Pagel, Christian Wey

February 2012

    IMPRINT  DICE DISCUSSION PAPER  Published by Heinrich‐Heine‐Universität Düsseldorf, Department of Economics, Düsseldorf Institute for Competition Economics (DICE), Universitätsstraße 1, 40225 Düsseldorf, Germany   Editor:  Prof. Dr. Hans‐Theo Normann Düsseldorf Institute for Competition Economics (DICE) Phone: +49(0) 211‐81‐15125, e‐mail: normann@dice.hhu.de    DICE DISCUSSION PAPER  All rights reserved. Düsseldorf, Germany, 2012  ISSN 2190‐9938 (online) – ISBN 978‐3‐86304‐043‐7   The working papers published in the Series constitute work in progress circulated to stimulate discussion and critical comments. Views expressed represent exclusively the authors’ own opinions and do not necessarily reflect those of the editor.    

Unionization Structures in International

Oligopoly�

Beatrice Pagely Christian Weyz

February 2012 (�rst version: October 2010)

Abstract

We examine how competition in international markets a¤ects a union�s choice of wage regime

which can be either uniform or discriminatory. Firms are heterogenous with regard to inter-

national competition. When unions choose their wage regimes sequentially, a discriminatory

outcome becomes more likely when international competition increases. However, for inter-

mediate levels a union may stick with a uniform wage regime even if the rival union adopts

a discriminatory regime. When competition is su¢ ciently intense, both unions revert to the

discriminatory regime. Paradoxically only in those latter instances all parties (consumers,

workers and �rms) may be better o¤ (each in aggregate) if all unions adopt a uniform wage

regime. We conclude that union incentives to coordinate their wage regimes should then

also become largest.

JEL-Classi�cation: D43, J51, L13.

Keywords: Unionization, International Oligopoly, Uniform Wages.

�We thank Justus Haucap, Annika Herr and seminar participants at the 2010 EARIE conference

for helpful comments. We gratefully acknowledge �nancial support by the German Science Foundation

(DFG) for the research project �Unionised Oligopolies.�

yHeinrich-Heine-Universität Düsseldorf, Düsseldorf Institute for Competition Economics (DICE);

email: pagel@dice.uni-duesseldorf.de.

zHeinrich-Heine-Universität Düsseldorf, Düsseldorf Institute for Competition Economics (DICE);

email: wey@dice.uni-duesseldorf.de.

1

1 Introduction

As globalization and economic integration have increased the competitive pressure in

international product markets, the impact of this trend on labor market organization has

become increasingly important. While there have been repeated demands for more wage

�exibility in response to increasing demand (and supply-) side pressure (see OECD 1996,

2006), empirical evidence on the development of labor market institutions towards more

decentralized wage bargaining structures is mixed.1

For some countries, such as Denmark and Sweden, there has been a clear tendency

towards more decentralization, other countries (e.g., Belgium and Italy) have witnessed a

higher degree of centralization in wage bargaining since the 1980s than at any other time in

the postwar period (Wallerstein and Western 2000). In a comparative study of 17 OECD

countries, Santoni (2009) shows that market integration has impacted negatively on the

level of wage bargaining. Similarly, in GermanyWest (East) the percentage of employment

contracts governed by centralized wage settlements has fallen from 70% (56%) in 1996 to

56% (38%) percent in 2009.2

The relation between market integration and trade costs on the one hand, and union

power on the other hand has received considerable attention in the literature (e.g., Brander

and Spencer 1988; Mezzetti and Dinopoulos 1991; Huizinga 1993; Munch and Skaksen

2002). However, in most models the degree of wage bargaining centralization is assumed to

be exogenously given (Dri¢ ll and van der Ploeg 1993, 1995; Naylor 1999).3 In contrast, we

endogenize the choice of wage-setting regimes by labor unions. Another critical departure

from previous works is that we consider heterogeneous �rms which are active in di¤erent

1We follow Calmfors and Dri¢ ll (1988), Moene and Wallerstein (1997), Flanagan (1999), and Waller-

stein (1999) to di¤erentiate national unionization structures according to the degree of wage setting

centralization. Under a decentralized structure wages are set between a single employer and the union

while the union negotiates a uniform wage for the entire industry under a centralized system.

2IAB Betriebspanel: �http://doku.iab.de/aktuell/2010/Tarifbindungsentwicklung_1996-2009.pdf�.

3An exception is Petrakis and Vlassis (2004) who analyze endogenous wage institutions at the national

level without considering international competition.

2

market environments.

The diversity of wage-setting institutions and their e¤ects in internationally integrated

product markets is analyzed in Corneo (1995). That paper examines the impact of dif-

ferent bargaining regimes when product markets are perfectly integrated. Besides other

things, it is shown that wages tend to be higher under a centralized bargaining structure

when compared with decentralized bargaining. Moreover, this tendency becomes more

pronounced when countries�sizes (in terms of national �rms) become more asymmetric.

The e¤ects of di¤erent labor market structures (varying in the degree of centralization)

on product market competition and market performance have been analyzed in many

works. One robust �nding is that the uniformity rule under a centralized union structure

can unfold bene�cial e¤ects for �rms�incentives to innovate or to set up new production

facilities (see Agell and Lommerud 1993; Leahy and Montagna 2000; Haucap and Wey

2004).4 Centralized wage-setting constrains the unions�ability to extract rents from �rms

which can be bene�cial for �rms and unions alike as it reduces hold-up problems associated

with union power.

Our paper analyzes a two-country model where national �rms operate in di¤erent

markets which gives rise to �rm-speci�c labor demands. We analyze the incentives of

labor unions to choose uniform or discriminatory wage-setting regimes in the presence of

international competition. On the one hand unions might prefer discriminatory wages

(which represents the adjustment of unionization structures to �rm-speci�c conditions) in

order to extract rents optimally from �rms enjoying di¤erent degrees of monopoly power.

On the other hand a uniform wage regime exhibits a commitment value when there is

international competition: if the e¤ect of a uniform wage is to raise the wage above the

discriminatory level in the international market, labor unions can bene�t from a �com-

petition dampening�e¤ect.5 Both a fully centralized or a partially centralized outcome

can emerge in equilibrium whenever international competition is not too strong. In the

4See also Mukherjee and Pennings (2011) who qualify that assertion by considering licensing.

5A similar e¤ect can occur in �nal goods markets when a retail chain adopts a uniform pricing policy

(see Dobson and Waterson 2008).

3

parlance of industrial organization a union choosing a uniform wage regime adopts a �fat

cat�strategy by committing to raise the wage level of the international �rm (Fudenberg

and Tirole 1984). As unions compete indirectly in wages (via the international �rms) a

uniform wage regime in country 1 induces a higher wage demand of the rival union in

country 2 because of strategic complementarity. The latter reaction is independent of

country 2�s wage regime so that an asymmetric outcome is possible where one country

adopts a centralized regime with uniform wages and the other country a decentralized

regime with wage �exibility at the �rm level.

Interestingly, a fully decentralized outcome emerges when international competition

becomes very intense. In those instances, we identify the possibility of a Pareto improve-

ment through international cooperation of unions�wage regime choices. That is, when

international competition is very intense, then each set of agents (i.e., unions, �rms and

consumers) bene�ts from a cooperative move towards uniform wage regimes. We, there-

fore, expect that international coordination of (national) wage setting regimes should

become more likely (and political feasible) when market integration further deepens.

Our paper proceeds as follows. In Section 2 we present an international oligopoly

model with two national and two international �rms. We characterize the equilibria un-

der di¤erent international unionization structures. Section 3 compares wage levels and

�rm pro�ts under three possible international unionization structures. Here, we also char-

acterize the possibility of a Pareto improvement through international union cooperation.

In Section 4 we solve for the equilibrium wage regime and we show that all international

unionization structures may emerge depending on the intensity of competition in the

international market. Finally, Section 5 concludes.

2 The Model

We consider a two-country model with two (heterogeneous) �rms in each country. All

�rms employ the same type of labor and they are active in di¤erent market environments.

We suppose that markets di¤er concerning their competitive intensity. There are three

4

separate markets: two national markets and a single international market. The national

market in each country, i = 1; 2, is served by a �rm Ni, with i = 1; 2. We suppose that

each national market is only served by a single domestic �rm; in particular, there is no

international competition in the national market.6 The (linear) demand in country i�s

national market is given by qNi(pNi) = 1� pNi, for i = 1; 2, where pNi is the price charged

by Ni.

In the international market two �rms I1 and I2 produce horizontally di¤erentiated

products and compete à la Hotelling. Firm Ii is located in country i. The two �rms face

a unit mass of consumers who are assumed to be uniformly distributed along the unit

line segment [0; 1]. We assume that �rms are located at the ends of the Hotelling line.

Consumers face transportation cost t > 0, which is assumed to be linear in the distance

between a consumer�s location on the line and the location of a �rm. Transportation costs

measure the intensity of competition between the �rms. The lower t the higher the degree

of competition in the international market.

The utility of a consumer located at location x and buying a product at price pIi from a

�rm located at xi is given by V (x; t; xi; pIi) = #�pIi�tjx�xij, where xi is equal to 0 (1) if

the consumer buys from international �rm I1 (I2). The parameter # denotes the constant

valuation of a consumer for the purchased product. We assume that # is su¢ ciently high,

so that the market is always covered in equilibrium. It is straightforward to determine the

demand faced by �rm Ii by identifying the indi¤erent consumer x = (pI2 � pI1 + t)=(2t)

from which we get the demand of �rm I1 and the demand of �rm I2 as qI1 = x and

qI2 = 1� x, respectively.

Firms operate under a constant returns to scale technology with respect to labor,

which is the only variable input for both national and international �rms. Without loss

of generality, we assume that qki = lki, for i = 1; 2 and k = N; I where qki is the output

and lki employment of �rm i in market k.

6Our results do not depend on our assumption that the national market is served by only a single

�rm. What is crucial for our results is that the competitive intensity di¤ers in the national and the

international market.

5

The workforce in each country is represented by a national labor union, union 1 and

union 2, which are responsible for wage setting in their respective countries. We apply

the right-to-manage approach which stipulates that a labor union sets the wage rate by

making a take-it or leave-it o¤er to the �rms. For given (and observable) wage rates, �rms

then determine their employment levels. We assume that each union maximizes its wage

bill.

The game proceeds as follows. In stage 1a, the union located in country 1 chooses

its wage regime. It can decide whether it wants to set discriminatory (D) or uniform

(U) wages for the two �rms in its country. Observing this choice, the union in country

2 determines its wage regime in stage 1b. In stage 2, the labor unions simultaneously

set their wage rates. Finally, in stage 3, �rms observe wage rates, and set prices for

their products. We solve the game by backward induction to derive subgame perfect Nash

equilibria.

Given that there are two rival unions who can determine their wage-setting regimes,

we have to consider three possible international unionization structures:

1. International Discriminatory (DD): Labor unions in both countries choose dis-

criminatory wage-setting regimes.

2. International Uniform (UU): Labor unions in both countries choose uniform wage-

setting regimes.

3. International Asymmetric (DU) or (UD): The �nal international unionization struc-

ture is asymmetric. One union chooses a discriminatory wage-setting regime, while

the rival union decides to apply a uniform regime.

We solve the model proceeding by backward induction for all three international union-

ization structures. In the last stage of the game, �rms set prices. National �rms have

local monopoly positions in their markets. The pro�t function of a national �rm is given

by

�Ni = (1� pNi) (pNi � wNi) , for i = 1; 2,

6

where wNi is the wage rate paid by national �rm i to each employed worker. Solving the

�rst order conditions @�Ni=@pNi = 0 yields the optimal price choices and the associated

quantities in stage 3

p̂Ni =1 + wNi2

,

q̂Ni =1� wNi2

. (1)

Simultaneously, the international �rms compete in prices. The pro�t function of �rm Ii

is given by

�Ii = (pIi � wIi) qIi, for i = 1; 2,

where wIi is the wage rate paid by �rm Ii to its employees. Solving the �rst order

conditions @�Ii=@pIi = 0 for i = 1; 2 yields the optimal prices and quantities

p̂Ii =3t+ 2wIi + wIj

3,

q̂Ii =3t� wIi + wIj

6t, (2)

with i 6= j. In stage 2 unions set wages for the workforce they represent in their respective

countries. The objective of each union in country i is to maximize its wage bill given by

Ui = (wNi l̂Ni) + (wIi l̂Ii), for i = 1; 2;

where the labor demands l̂Ni and l̂Ii follow from (1) and (2), respectively. According

to the wage-setting regimes unions have determined in the �rst stage of the game, we

have to consider the three international unionization structures DD, UU , and UD=DU

separately.

International Discriminatory (DD). Assume that both unions have adopted discrim-

inatory wage regimes. In this case, the optimal wage rates set by each union are given by

the solution of

fwDD�Ni; wDD�Ii

g = argmaxwNi ;wIi

Ui(wNi ; wDD�Nj

; wIi ; wDD�Ij

), for i; j = 1; 2, i 6= j.

7

Using (1) and (2) and solving the respective �rst order conditions @Ui(�)=@wIi = 0 and

@Ui(�)=@wNi = 0 for i = 1; 2 yields the following equilibrium wage rates charged to the

national and the international �rm, respectively:

wDD�N =1

2and wDD�I = 3t.

Note that equilibrium wages are identical under scenario DD for t = 1=6. In this case,

the unionization structure collapses to the case were both unions set uniform wages. Note

that the wage charged to the international �rm becomes larger than the wage of the

national �rm if international competition is relatively weak (i.e., t > 1=6 holds), while the

opposite is true if competition is su¢ ciently strong (i.e., t < 1=6 holds).

International Uniform (UU). Consider that both unions have adopted uniform wage-

setting regimes so that the outcome is an international uniform unionization structure.

In this case, a uniform wage rate wNi = wIi = �wi is set by each union to maximize the

total wage bill. The optimal wage rate each union sets is the solution to

f �wUU�i g = argmaxwi

Ui(wi; �wUU�j ), for i; j = 1; 2, i 6= j.

Again, we solve the �rst order conditions @Ui(�)=@wi = 0 for i = 1; 2 using (1) and (2) to

obtain the equilibrium wage rate each union sets; namely,

�wUU� =6t

1 + 6t.

Obviously, national �rms are now a¤ected by the degree of competition in the international

market. When international competition becomes more intense (i.e., t decreases), then

the uniform wage level decreases for both the national and the international �rm. Note

that wDD�N = wDD�I = �wUU� is true at t = 1=6.

International Asymmetric (DU) or (UD). Finally, we analyze the case when one

union has adopted a discriminatory wage regime while the other union chooses to set

uniform wages. The timing of our game postulates that the union located in country 1

chooses its wage wage regime �rst, with the union located in country 2 following. Let

8

us assume at this point that union 1 adopts the discriminatory regime in an asymmetric

outcome. Below in Section 4, we will show that whenever the asymmetric unionization

structure is an equilibrium outcome, the union which determines its wage regime �rst will

choose discrimination.

Given that union 1 has adopted a discriminatory regime in stage 1a, it sets discrimi-

natory wages in stage 2 which solve

fwDU�N ; wDU�I g = argmaxwN1 ;wI1

U1(wN1 ; wI1 ; �wDU�2 ).

When the �nal unionization structure is asymmetric, union 2 has obviously opted for a

uniform wage regime in stage 1b. In stage 2, union 2 sets a uniform wage rate to maximize

its wage bill which solves

f �wDU�g = argmaxw2

U2(w2; wDU�N ; wDU�I ).

Solving the set of three �rst order conditions, the equilibrium wage rates set by unions 1

and 2 are

wDU�N =1

2,

wDU�I =t(4 + 6t)

1 + 4t, and

�wDU� =5t

1 + 4t.

Note that, in contrast to the previous international unionization structures, �rms com-

peting in the international market will now face di¤erent labor costs. Which international

�rm pays the higher wage rate and thus obtains a lower pro�t than its rival will depend

on the intensity of competition in the international market.

We solve for the equilibrium pro�ts, wage bills, prices and consumer surplus for the

three unionization structures in the Appendix. Before we analyze the equilibrium choices

of wage regimes of the labor unions, we can compare the e¤ects of di¤erent forms of

unionization structures on unions and �rms.

9

3 The Impact of Unionization Structures on Wages

and Pro�ts

We begin with an analysis of the di¤erent international unionization structures. Having

solved for the wage rates and pro�t levels of �rms, we can compare them under the

di¤erent structures. Therefore, we abstract from the labor unions choices of wage-setting

regimes in stages 1a and 1b and treat them as given for the moment. To some extent,

an exogenous determination of wage-setting regimes has been present in many European

countries where wage bargaining between labor unions and �rms has been institutionalized

through labor market regulations and/or social norms. Institutional change, e.g., from an

egalitarian wage system towards a more �exible, and hence, discriminatory wage regime

comes not overnight but rather is the result of a transformation process which may take

decades.7

3.1 Wages

The following Lemma summarizes the results of the comparison of wage levels.

Lemma 1. The ranking of wage rates within di¤erent market structures depends on

the intensity of competition in the international market and the prevailing unionization

structures:

i) If the intensity of competition in the international market is low, i.e., t > 1=6 holds,

then wDD�I > wDU�I > �wDU� > �wUU� > wDD�N = wDU�N .

ii) If the intensity of competition in the international market is high, i.e., if t < 1=6

holds, then wDD�N = wDU�N > �wUU� > �wDU� > wDU�I > wDD�I .

7In Germany, the dominant industry unions of the Deutsche Gewerkschaftsbund (as, e.g., IG Metall)

strictly opposed any form of wage �exibility for at least twenty years; a position which was eventually

given up in the last decade of the last century when opting out and opening clauses became widely

adopted elements of collective agreements (see Haucap, Pauly, and Wey 2007).

10

Moreover, equality holds with wDD�I = wDU�I = �wDU� = �wUU� = wDD�N = wDU�N for

t = 1=6.

The interpretation of Lemma 1 is straightforward. Independent of the degree of com-

petition in the international market, the level of uniform wages ( �wUU� or �wDU�) lies

inbetween the discriminatory wage levels. This is the averaging e¤ect of uniformity: each

labor union optimally sets the uniform wage rate such that asymmetries between the �rms

are balanced.

In which market the highest (lowest) wage rates are paid by �rms, depends on the

intensity of competition between the international �rms. For a low degree of competition,

i.e., case i) holds, national �rms pay the lowest (discriminatory) wages and international

�rms pay the highest wage rates.

This is the case because, from a labor union point of view, the international market is

the �larger�market when t > 1=6. Obviously, the (discriminatory) wage rates are directly

related to competitive pressure in this market: @wDD�I =@t > 0 (likewise @wDU�I =@t > 0),

i.e., the larger the market power of the international �rms, the more rent a labor union can

extract from the �rms. For t > 1=6, the degree of international competition is su¢ ciently

low so that the unions will set discriminatory wages in this market which exceed the wage

levels paid by national �rms.

Note that, while the discriminatory wage rates paid by national �rms in structuresDD

and DU are identical, the same is not true for the wage rates of the international �rms,

as wDD�I > wDU�I . This is due to the asymmetry in wage levels structure DU implies. As

wage regimes are determined by the labor unions before the actual wage rates are set,

each union knows which kind of wage behavior its rival displays. In structure DU , the

discriminating union knows that its rival sets a uniform wage, which must optimally be

lower than a discriminatory wage because of the averaging e¤ect described above. As a

consequence, the discriminating union will set a wage wDU�I < wDD�I because otherwise

the international �rm would lose too much of a market share vis-à-vis its competitor

operating at lower wage costs.

11

For high intensity of competition in the international market, i.e., t < 1=6, the order of

wage rates is reversed. From the point of view of a labor union, the international market

is now the small market compared to the national market. Consequently, discriminatory

wage rates paid by national �rms will be highest, while those paid by the international

�rms in structure DD are lowest. The averaging e¤ect of uniformity implies that levels

of uniform wage rates (either in structure UU or DU) will be inbetween.

Note that the ordering of the two uniform wage rates is now reversed as well: �wUU� >

�wDU�. In unionization structure DU , the uniform wage regime of union 2 now exhibits a

commitment e¤ect : a union setting the uniform wage in an asymmetric structure knows

that it will put the �rm paying �wDU� at a disadvantage in product market competition be-

cause the averaging e¤ect of uniformity will cause the wage rate paid by the international

�rm to increase compared to a discriminatory level. Consequently, �rm I2 will behave

less aggressively in the international market.

Union 1 can partially free-ride on this e¤ect: it can raise its discriminatory wage rate

wDU�I above the purely discriminatory level, because wages are strategic complements for

the labor unions, and �rm I1 will still capture more than half of the international market,

because it can price more aggressively than its competitor due to lower input costs. Here,

union 1 gains twice: �rst through an increase of the wage level charged to the international

�rm and second through a higher level of employment.

3.2 Pro�ts

The comparison of pro�ts shows that �rms are not only a¤ected by the wage regime of

the union in their home country, but also by that of the foreign union through the link of

product market competition.

Lemma 2. The pro�t levels of �rms depend on the intensity of competition in the inter-

national market and the prevailing unionization structures:

i) If the intensity of competition in the international market is low, i.e., t > 1=6 holds,

then the ordering of pro�ts of the national �rms and the international �rms is given by

12

�DD�N1= �DU�N > �UU�N > �DU�N2

and �DU�I2> �UU�I = �DD�I > �DU�I2

, respectively.

ii) If the intensity of competition in the international market is high, i.e., if t < 1=6

holds, then the ordering of pro�ts of the national �rms and the international �rms is given

by �DU�N2> �UU�N > �DD�N = �DU�N1

and �DU�I1> �UU�I = �DD�I > �DU�I2

, respectively.

Moreover, equality holds with �DD�N1= �DU�N = �UU�N = �DU�N2

for t = 1=6.

The intuition behind Lemma 2 is straightforward and can be summarized as follows.

From the above analysis we know that the international market is the �large�market

from the point of view of labor unions, when t > 1=6. A uniform wage, therefore, lowers

the wage rate paid by an international �rm. As pro�ts must be identical for symmetric

unionization structures, an interesting point arises when the unionization structure is

asymmetric.

For t > 1=6, national �rms prefer discriminatory wages in their home country, as

the averaging e¤ect of uniformity would cause higher wage rates for them compared to

a discriminatory level. Comparing the pro�ts of a national �rm in structures UU and

DU when the �rm pays a uniform wage, we �nd that a �rm prefers international uniform

unionization over an asymmetric structure. Although the national �rm faces no interna-

tional competition, its pro�ts are lower when the foreign union adopts a discriminatory

regime when in the home country a uniform wage regime is in place.

This is the case, because the uniform wage rate is higher in the asymmetric structure

DU than when both unions choose a uniform regime. The discriminating union sets a

high discriminatory wage in the international market, thereby dampening competition and

giving an incentive for the rival union to set high uniform wage rate �to the detriment

of the national �rm.

In part ii) of Lemma 2, the ordering or pro�t levels according to unionization structures

is reversed for both national and international �rms. Obviously, this depends on the fact

that for t < 1=6 the national market becomes the �large�market for the labor unions.

National �rms paying discriminatory wage rates will earn the lowest pro�ts in com-

parison to paying uniform wage rates, as they cannot bene�t from the intense competitive

13

conditions in the international market. Instead, labor unions will �nd it optimal to set high

wage rates in the national markets and extract high rents from these �rms. If competition

in the international market is intense, national �rms should support the introduction of

uniform wages.

Obviously, the two symmetric international unionization structures DD and UU will

yield the same pro�t levels to the two international �rms due to the speci�c functional

forms, but pro�ts will now be highest in a DU structure for the �rm paying a discrimi-

natory wage and earning �DU�I1 and consequently lowest for the �rm paying the uniform

wage rate and obtaining �DU�I2:

In this setting, the labor union opting for the uniform wage regime will set a wage

�wDU� which is higher than a discriminatory wage rate and thus reduces the competitive

pressure in the international market. A uniform wage regime displays a commitment

value: the labor union opting for the discriminatory wage regime will set a wage rate

lower than �wDU� which enables the �rm to serve more than half of the international

market. However, due to the uniform wage regime of the other union, it will not set an

excessively low wage, so that wDU�I > wDD�I prevails. Consequently, the pro�ts obtained

by the �rm paying the discriminatory wage rate in structure DU , �DU�I1 , are highest while

those of the �rm paying the uniform wage rate, �DU�I2, are lowest.

The comparison of pro�ts and wage rates shows that either of the three international

unionization structures can result in higher or lower wage rates and �rm pro�ts, depending

on the intensity of competition in the international market. Foremost, we are interested

in the opportunity for labor unions to refrain from setting discriminatory wage rates

for heterogeneous �rms and to opt for a uniform wage regime instead when there is

international competition.

Taking wage bills, pro�ts and consumer surplus into account, we can show that it is

possible that �rms, labor unions and consumers are better o¤ (each in aggregate) under

an international uniform structure than under a discriminatory unionization structure.

As the following Proposition states, this can only occur when the international market is

14

the �small�market from the unions�perspective.

Proposition 1. If the intensity of competition in the international market is relatively

strong, so that t < 1=6 holds, then there exists a range of parameter values t 2 ((p17 �

3)=24; (p145� 7)=96), such that labor unions, �rms and consumers are each in aggregate

better o¤ under an international uniform than under an international discriminatory

unionization structure.

Proof. See Appendix.

If competition is su¢ ciently intense in the international market the averaging e¤ect of

a uniform wage will induce the wage rate paid by the �rms in the international market to

rise while that of the national �rms will fall. Only if this is the case producer surplus will

be higher under an international uniform structure (UU). National �rms gain through

lower wage rates caused by the intense competition in the international market.

Consumer surplus will only increase if the gain of consumers in the national market

can o¤set the loss in consumer surplus in the international market due to a higher price. A

prerequisite is that competition in the international market is su¢ ciently intense so that

the increase in labor costs (and consequently consumer prices) is su¢ ciently moderate.

The less market power the �rms have, the more limited is the power of a labor union to

increase the wage rate in the given market. The condition for consumers to be better o¤

on aggregate is therefore given by t < (p145� 7)=96.

This is the upper threshold on parameter t derived in Proposition 1. For any t >

(p145�7)=96 consumers as a whole will not bene�t through a joint uniform unionization

structure. Wage (and price) increases in the international market would be too high.

Finally, labor unions gain if markets are not too heterogeneous, i.e., if the increase in

the wage rate in the international market can compensate for the decrease in the wage

rate paid by the national �rms. Wages in the international market can only be increased

su¢ ciently if �rms have enough market power, i.e., if competition is not too intense which

yields the lower bound on the transportation cost parameter t stated in Proposition 1;

namely (p17� 3)=24 < t.

15

For any t < (p17 � 3)=24, labor unions cannot raise the wages in the international

market su¢ ciently to o¤set the loss in wage bill through lower national wage rates.

We are aware of the fact that this result hinges upon the functional forms used in

our example. Nevertheless, we observe that there is scope for uniform wage regimes by

unions to be bene�cial not only for the labor unions themselves, but also for �rms and

consumers. Quite intuitively, this is likely to be the case when international competition

puts downward pressure on collective wage agreements (i.e., t < 1=6 holds). Moreover,

international competition must not be too strong as this would induce unions to revert to

discriminatory wage regimes that aim at extracting rents from the remaining monopoly

power in national markets.

4 Equilibrium Wage-Setting Regimes

Although wage-setting structures seem to be rather rigid institutions, recent changes

suggest that in the long-run wage-setting regimes can be adapted by labor unions. When

we endogenize the decision on wage-setting regimes, we are able to analyze the incentives

for labor unions to opt for either a uniform or a discriminatory wage regime.

This decision is particularly interesting, when unions have the opportunity to observe

and react to the wage regimes of labor unions in foreign countries, anticipating that the

own wage regime choice will a¤ect a �rm�s stand in international competition.

We analyze this choice sequentially to incorporate the option that labor unions react

to the wage-setting regimes by foreign rivals. We have solved for the �nal wage bills

obtained by labor unions in each unionization structure in the Appendix. Table 1 presents

the choice of the labor unions in the �rst two stages 1a and 1b of the game between either

uniform (U) or discriminatory (D) in a reduced form, indicating the associated wage bill

levels, a union will obtain for either choice.

To �nd the equilibrium choice of wage regime, we need to consider two wage bill

comparisons: namely union 2 choosing a discriminatory or a uniform wage-setting regime,

given that union 1 has either adopted a discriminatory or a uniform regime. From Table 1

16

it is straightforward to determine the preferences of the two labor unions for either wage-

setting regime and to calculate the subgame-perfect equilibrium wage regime choices.

Union 1 n Union 2 D U

D UDD�1 , UDD�2 UDU�1 , UDU�2

U UUD�1 , UUD�2 UUU�1 , UUU�2

Table 1. Normal Form Representation of the Wage Regime Choices

We �nd that the equilibrium wage regimes -and therefore the international unionization

structures which will result in equilibrium- depend on the intensity of competition in the

international market.

Proposition 2. If labor unions choose their wage-setting regimes sequentially, then there

exist critical values 0 < t < t0 < t := 1=6 such that the resulting international unionization

structures (DD, UU, DU) can be sustained as equilibrium unionization structures:

i) If t 2 (0; t) [ (t;1), then the unique equilibrium unionization structure is interna-

tional discriminatory (DD).

ii) If t 2 (t; t0), then the resulting unionization structure is international asymmetric

(DU), where the �rst union adopts a discriminatory wage regime.

iii) If t 2 (t0; t), then the unique equilibrium unionization structure is international

uniform (UU).

Proof. See Appendix.

Any of the three international unionization structures analyzed in this paper can occur

in equilibrium depending on the value of the transportation cost parameter t. For t 2 (0; t)

and t 2 (�t;1) the equilibrium unionization structure is given by DD. When competition

intensity is very high or very low between the international �rms, both unions will �nd

it bene�cial to choose a discriminatory wage regime to extract as much rent as possible

from the �rms. In such a case, �rms are so heterogenous that labor unions do not �nd it

bene�cial to forego a higher wage rate in one market in order to obtain a higher wage in

17

the other. If competition is too intense, a union could not pro�tably raise the international

wage rate through uniformity to o¤set the loss due to a lower wage rate in the national

market.

Note that the interests of �rms and labor unions are only partially aligned here. If

t 2 (�t;1), national �rms prefer discriminatory wages just as unions do. As we showed in

the previous section a uniform wage would cause a rise in wage for the �rms (compared to

the discriminatory level) and therefore lead to lower pro�ts. If, however, t 2 (0; t), national

�rms would prefer uniform wages in order to bene�t from the intense competition in the

international market through a lower wage level. This preference is contrary to that of

the labor unions.

For an intermediate degree of competition in the international market, both unions

prefer uniform wage-setting regimes. If �rms are not too heterogenous labor unions will

bene�t from a uniform wage. As t < �t := 1=6, the averaging e¤ect of uniformity will work

in the direction that the wage rate paid by international �rms is higher, and that paid by

national �rms lower than if both unions had adopted discriminatory wage regimes. The

gain for the union through setting a higher international wage rate here is large enough

to compensate for the lowered wage rate in the national market.

From the viewpoint of a labor union, it can make sense not to exploit the di¤erences

in competitive conditions in the two product markets through discriminatory wages. The

presence of international competition (and a rival union) in one of the markets adds a

strategic motive to the choice of uniform wages. Obviously, a labor union will be willing

to sacri�ce its freedom to discriminate between markets if the losses in the wage bill due

to a lower wage in one market will be o¤set by the higher income from the other market.

As wages are strategic complements among unions, a choice of a uniform wage regime will

have the e¤ect of dampening competition in the international market for t < �t:

Finally, for t 2 (t; t0) we obtain an asymmetric equilibrium unionization structure

where one union sets a discriminatory wage and the other sets a uniform wage. Note

that a comparison of wage bills yields that in such a situation, the union setting the

18

discriminatory wage obtains a higher wage bill than the one setting the uniform wage.

Consequently, in an asymmetric equilibrium resulting in unionization structure DU , it

will be the union which has the �rst mover advantage (union 1) which will choose the

discriminatory wage-setting regime. The rival union 2 will respond with its best reply in

stage 1b: choosing a uniform wage regime.

Again, we can observe the commitment e¤ect of uniformity: union 2 adopting a uni-

form wage-setting regime commits itself to set a relatively high wage rate, thereby provid-

ing a basis for the rival union to set a discriminatory, but higher wage rate than it would

have been optimal if both unions had adopted discriminatory wage regimes. Both unions

gain: the union which discriminates will set a wage rate such that the �rm paying it will

serve more than half of the international market. The labor union committed to unifor-

mity will optimally set a higher uniform wage compared to unionization structure DD.

Union 1 setting the discriminatory wages can free-ride on the dampening of competition

in the international market union 2 provides.

We analyzed the e¤ects on �rms�pro�ts in Section 3. A uniform wage regime by one

union will su¢ ce to reduce the competitive pressure in the international market. Since

�rms can perfectly observe the wages set by both unions, an international �rm paying a

discriminatory wage will respond to an increased labor cost of its rival by a higher price

in the product market. Therefore, competitive pressure is reduced and the union setting

uniform wages will gain from a uniform wage regime which dampens competition.

A comparison of the equilibrium unionization structures with the results of the previ-

ous section reveals that labor union preferences and consumer interests are not aligned.

Although consumers and labor unions would be better o¤ in structure UU for t 2

((p17 � 3)=24; (

p145 � 7)=96), unions will choose discriminatory wage regimes, if they

determine them non-cooperatively, resulting in unionization structure DD. This problem

could be resolved if unions were able to coordinate their wage-setting regimes interna-

tionally and form a joint international unionization structure. This result is in line with

the observation that labor unions have increased their activities on the European level

19

(Schulten, 2002) to coordinate wage-setting regimes; an initiative which obviously mirrors

increasing competitive pressure in international markets.

5 Conclusion

The model presented in this paper provides an analysis of labor union preferences for

discriminatory or uniform wage regimes vis-à-vis heterogeneous �rms when national la-

bor market institutions are linked through international competition in product markets.

Although the model is based on speci�c functional forms, its implications may contribute

to a better understanding of the development of labor market institutions.

With heterogeneous �rms, a comparison of discriminatory and uniform wage-setting

regimes reveals the averaging e¤ect of uniformity we have analyzed above. As presented

in our model, labor unions have to compare the bene�ts through an increased wage rate

for one type of �rm to the loss through a reduced wage rate paid by the other.

In a more general model, we could therefore observe this trade-o¤ for labor unions,

though the scope for an international uniform unionization structure would be less obvious.

Nevertheless, we have characterized a situation in which unions, �rms and consumers as

a whole gain through uniform wages in both countries. Interestingly, such a constellation

is only likely if international competition puts downward pressure on collective wage

agreements.

An important insight of our model refers to the pro�tability of a uniform wage-setting

regime to unions even if a rival union has adopted a discriminatory wage regime. This

commitment e¤ect of uniformity is not new, but supports the observation that labor

unions stick to centralized, uniform wage bargaining structures even when labor markets

in foreign countries are more �exible and allow for undercutting regimes.

The commitment value of uniformity by one union provides a basis for the other union

to set a discriminatory wage above the level of an international discriminatory unionization

structure. In turn, the former will slightly bene�t from this lessening in competition in

terms of wage bill rents. In the sequential order of wage regime choices, the union which

20

moves �rst is clearly in the better position: it will optimally choose the discriminatory

wage regime since it correctly anticipates that the other union will respond with a uniform

wage regime.

A comparison with the results from Section 3 suggests that consumer and union pref-

erences are not aligned. Although consumers and labor unions would be strictly better

o¤ in structure UU for t 2 ((p17 � 3)=24; (

p145 � 7)=96), non-cooperative decisions

of labor unions over wage-setting regimes will result in an international discriminatory

unionization structure. An international coordination of labor unions over wage regimes

as described by Schulten (2002) could resolve this problem.

21

Appendix

We solve our model for the three di¤erent unionization structures DD, UU , and DU . In

the main part of this paper, we derived the wage levels. In this Appendix we present the

solutions for pro�ts, wage bills, and consumer surplus.

International Discriminatory (DD):

�DD�N =1

16; (3)

�DD�I =t

2; (4)

UDD� =1

8+3t

2; (5)

CSDD�N =1

32; (6)

CSDD�I = #� 4t: (7)

International Uniform (UU):

�UU�N =1

4(1 + 6t)2(8)

�UU�I =t

2(9)

UUU� =6t (1 + 3t)

(1 + 6t)2(10)

CSUU�N =1

8 (1 + 6t)2(11)

CSUU�I = #+1

1 + 6t� 1� t (12)

International Asymmetric (DU):

In the labor union in country 1 adopts a discriminatory wage-setting regime:

�DU�N1 =1

16,

�DU�I1 =2t(2 + 3t)2

9(1 + 4t)2,

UDU�1 =3 + 8t[11 + 6t (5 + 3t)]

24(1 + 4t)2. (13)

22

The labor union in country 2 adopts a uniform wage-setting regime:

�DU�N2 =(t� 1)24(1 + 4t)2

,

�DU�I2 =2t(1 + 9t)2

9(1 + 4t)2,

UDU�2 =25t (1 + 3t)

6 (1 + 4t)2. (14)

Proof of Proposition 1. The proof of Proposition 1 follows immediately from the

comparison of wage bills, pro�ts and consumer surplus under the international uniform

and international discriminatory unionization structures. A labor union will only be

better o¤ under UU if it earns a higher wage bill than in a DD structure, i.e., �U =

UUU� � UDD� > 0. Using (5) and (10) we obtain 18

h3� 12t� 4

(1+6t)2

i> 0. Solving this

expression for t we �nd that the inequality is ful�lled for (p17� 3)=24 < t < 1=6.

For �rms to be better o¤ under UU , we have to verify that producer surplus exceeds

that under DD. Since �UU�I = �DD�I , it is su¢ cient to show that �� = �UU�N ��DD�N > 0.

Using expressions (3) and (8) and solving for t, we �nd that �rms are on aggregate better

o¤ under a uniform structure for 0 < t < 1=6.

Finally, we analyze when overall consumer surplus increases, is that �CS = CSUU�I +

2CSUU�N � (CSDD�I + 2CSDD�N ) > 0 holds. Substituting (6), (7), (11) and (12), we obtain

that consumers are better o¤ if 0 < t < (p145� 7)=96 or t > 1=6. Analyzing the above

obtained results, it is easy to see that there exists a range of values of the transportation

cost parameter where unions, �rms, and consumers are better o¤ under UU than under

structure DD. This is the case, whenever (p17� 3)=24 < t < (

p145� 7)=96 holds.

Proof of Proposition 2. Again, the proof of Proposition 2 involves a comparison of

the wage bills the unions obtain under all three unionization structures. Using (5), (10),

(13) and (14), the unions�decision problems in stages 1a and 1b can be displayed by the

reduced form game presented in Table 1.

Comparing the resulting wage bills, we �nd that the equilibrium unionization structure

depends on the intensity of competition in the international market.

Suppose union 1 chooses D in stage 1a, international discriminatory (DD) will be an

23

equilibrium structure only if UDD��UDU�2 > 0; i.e., if 18+3t2� 25t(1+3t)

6(1+4t)2> 0. The di¤erence

UDD��UDU�2 has three roots of which only two are feasible; namely, t := (p409� 11)=96

and t := 1=6. These solutions give rise to the result stated in part i) of the Proposition;

namely, that DD is the equilibrium union structure, if t 2 (0; t) or if t 2 (t;1).

Similarly, we can determine when uniformity is a best response for union 2 given that

the union 1 has chosen a uniform wage-setting regime. This is the case when UUU� �

UDU�1 > 0. The sign of the di¤erence UUU� � UDU�1 is given by the sign of the expression

5184t5 + 3456t4 + 432t3 � 180t2 � 20t+ 3.

That expression has only two feasible real roots; namely, 1=6 and t0 :� 0:10112 (the

latter solution is derived numerically). It is now easily checked that UU is the unique

equilibrium union structure for t 2 (t0; t).

We, �nally, determine when unions prefer an asymmetric outcome. This is the case

when both conditions UDU�1 � UUU� > 0 and UDU�2 � UDD� > 0 hold. It then follows

from our previous results, that an asymmetric union structure emerges in equilibrium for

t 2 (t; t0). Comparing the unions�wage bills (13) and (14) we obtain that the di¤erence

UDU�1 � UDU�2 has two roots, 1=6 and 1=2, and obtains a global minimum at t = 1=3. As

DU is only an equilibrium outcome for t 2 (t; t0), we can conclude that UDU�1 �UDU�2 > 0.

Hence, the union which possesses the �rst mover advantage regarding the choice of wage-

setting regime always selects a discriminatory regime. Finally, the ordering of the critical

values ful�ll 0 < t < t0 < t := 1=6.

24

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